What is the length of the curve

Question

What is the length of the curve from y = 0 to y = 1?

Answer 1

dx/dy = (1/3) (3/2)(2y)(y²+2)^1/2

(dx/dy)² + 1 = y⁴ + 2y² + 1 = (y² + 1)²

S(y) = ∫y² + 1dy from 0 to 1, since √(y² + 1)² = y² + 1

= y³/3 + y from 0 to 1 = 4/3